14 1. Differential Equations Figure 1.6-1: A demonstration of the use of the MyAnimate command for a function of one spatial and one temporal variable. MyAnimate[f_, {x,x0_,x1_}, {y,y0_,y1_}, {z,z0_,z1_}, {t,t0_,t1_}, n_] := ListAnimate[Table[Plot3D[f, {x, x0, x1}, {y, y0, y1}, PlotRange - {z0, z1}], {t, t0, t1, (t1 - t0)/n}]] To use the command to animate a function f(x, t) of one spatial and one temporal variable, you choose a viewing window (x0 ≤ x ≤ x1, y0 ≤ y ≤ y1) and a time interval (t0 ≤ t ≤ t1) and determine the number of frames you want (n) with the understanding that more frames produce a smoother movie but also require more computer power. The command MyAnimate[f[x,t],{x,x0,x1},{y,y0,y1},{t,t0,t1},n] should then produce the desired animation. Similarly, for a func- tion f(x, y, t) with two spatial variables, one can graph an animated surface by saying MyAnimate[f[x,y,t],{x,x0,x1},{y,y0,y1},{z,z0,z1}, {t,t0,t1},n] where the three-dimensional viewing “box” is specified by the inter- vals in x, y and z. Some homework questions below will give you an opportunity to test your ability to use these commands.
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